In the circle K, what is the value of x?

options: x= 30dg,25dg,20dg, or 15dg.

What is the measure of (Arc symbol) AC?

KenyaT.
Mar 7, 2017

#1**0 **

We have a right angle with the diameter as a hypotenuse....the other two angles are complementary.....so x = 15°

The inscribed angle is (1/2) of its intercepted arc

So

(4x + 3.5) = (1/2)(4x + 17) multiply through by 2

2 (4x - 3.5) = (4x + 17)

8x - 7 = 4x + 17 add 7 to both sides, subtract 4x from each side

4x = 24 divide both sides by 4

x = 6

So AC = 4(6) + 17 = 24 + 17 = 41°

CPhill
Mar 7, 2017